Various surface extensions are observed in many cell processes. For example, the reversible disc-sphere transformation of a red blood cell has an intermediate form of a crenated sphere. Here a continuum approach is proposed to model that part of the transformation which is from a sphere to a crenated sphere. The interior of the cell (hemoglovin) can be viewed as a viscous incompressible fluid, while the membrane is modelled by a visco-elastic fluid or solid. When the exterior environment of the cell is changed causing the addition of proteins or chemicals into the membrane, protuberances begin to form on the spherical surface. The model allows a mathematical study of the response of an encapsulated droplet to changes in the membrane. The relative importance of the viscous and elastic properties, and surface tension and the bending moments of the membrane will be determined by comparing the rates of growth, number and size of the ruffles that are proposed theoretically for a droplet with the actual crenations which are observed. Protuberances often occur at local sites on the surface (myelin forms), or in the case of the disc - sphere transformation, always reappear in the same position. These may be caused by local binding of material or a change in chemical composition in the membrane, which necessarily causes a change in the surface tension. A study of the response of a droplet to local source terms will be initiated. The continuum approach requires the formulation of equations of motion, conservation of mass and balance of stresses arising from viscous, elastic and surface tension forces. The resulting system is a moving boundary value problem, that is, the equation for the boundary of the droplet as well as the motion of the fluids must be solved simultaneously. the dynamical instabilities which arise reveal the modes of largest growth and the resulting shape of the droplet. The proposed research will provide a better understanding of the dynamical basis for the crenation of the red blood cell. It will also indicate that most important components that control its characteristics and time scales. This is important for an understanding of the membrane structure of red blood cells and their ability to deform into restricted regions of the microcirculation. It may also apply to the deformed red cells that are apparent in many blood diseases.